Abstract
The properties of $\mathrm{\ensuremath{\Delta}}$ isobars in a uniform magnetic field are investigated. General relations between the magnetic moments of nucleons and $\mathrm{\ensuremath{\Delta}}$ isobars in a weak magnetic field are given. In a strong magnetic field, the masses and sizes of $\mathrm{\ensuremath{\Delta}}$ isobars depend on the magnetic field strength in different ways: the effective masses of ${\mathrm{\ensuremath{\Delta}}}^{++}$, ${\mathrm{\ensuremath{\Delta}}}^{+}$, and ${\mathrm{\ensuremath{\Delta}}}^{0}$ (the sizes of ${\mathrm{\ensuremath{\Delta}}}^{++}$ and ${\mathrm{\ensuremath{\Delta}}}^{+}$) first decrease (increase) and then increase (decrease), whereas the effective mass of ${\mathrm{\ensuremath{\Delta}}}^{\ensuremath{-}}$ (the sizes of ${\mathrm{\ensuremath{\Delta}}}^{0}$ and ${\mathrm{\ensuremath{\Delta}}}^{\ensuremath{-}}$) always increases (decrease). Our estimates show that, in the core part of the magnetar, the equation of state for $\mathrm{\ensuremath{\Delta}}$ isobars depends on the magnetic field, which affects the upper limit on the mass of the magnetar.
Highlights
The Δ isobars play a very important role in nuclear physics [1]
Since Δ isobars have internal structure, the properties of Δ baryons could be dramatically changed by the strong magnetic fields that widely exist in heavy-ion colliders and magnetars [5,6,7]
The masses, magnetic moments, and mean square (MS) electric charge radii of Δ isobar states in a uniform magnetic field were studied in the semiclassical quantization approach of the Skyrme model
Summary
The Δ isobars play a very important role in nuclear physics [1]. For example, a Δ baryon medium exists in heavy-ion colliders [2] and neutron stars [3,4]. Since Δ isobars have internal structure, the properties of Δ baryons could be dramatically changed by the strong magnetic fields that widely exist in heavy-ion colliders and magnetars [5,6,7]. The magnetic responses of Δ baryons could be measured in a heavy-ion collider or in a magnetar. The sizes of Δþþ and Δþ first become larger and smaller, whereas the sizes of Δ0 and Δ− always become smaller Since both the masses and sizes of Δ isobars depend on the strength of the magnetic field, the equation of state for Δ isobars is influenced by the magnetic field, which could affect the properties of magnetars
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